In the practice of medicine, many instruments are used that require different fluid (i.e. gaseous or liquid) media, for example, compressed gases, water, or the like. In order to supply the fluid to the instruments, the instruments are connected by way of a fluid connector to an appropriate medical apparatus that provides the fluids in the desired state and in the desired quantity. In doing so, the fluids may be under considerable pressure, which is the case in cryosurgical applications. In a still relatively simple case, the appropriately pressurized cryogenic fluid must be supplied to the instrument, and the depressurized cryogenic fluid must be carried away. To accomplish this, two separate fluid lines are required. In many cases, a third fluid line for the additional return of the cryogenic fluid is required, for example when the freezing process was interrupted and the thawing process is to be accelerated. In this case, it is possible to add additional fluid lines for fluids that are required for the treatment process.